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Identifying proportional relationships
Description
Exercise Name: Identifying proportional relationships
Math Missions: 7th grade (U.S.) Math Mission
Types of Problems: 3

The Identifying proportional relationships exercise appears under the 7th grade (U.S.) Math Mission. This exercise introduces has several problems that attempt to help the user better understand direct variation.

## Types of Problems

There are three types of problem in this exercise:

1. Determine if the relationship is proportional: This problem provides a given graph, chart or word problem and asks the user to determine whether they relationship is proportional or not. The answer is given in a multiple choice format.
2. Fill in missing information and determine if the relationship is proportional: This problem provides information and a partially filled in chart, or T-table. The user is asked to complete the missing information and determine if the relationship is proportional.
3. Create graph and determine if the relationship is proportional: This problem has a grid on which the user is asked to create a graph representing some information. In addition, users are asked to determine if the given relationship is proportional or not.

## Strategies

This concept is almost identical to direct variation, so knowledge of direct variation will assist with doing these problems correctly.

1. It is said that ${k}$ varies directly with ${x}$ if ${y=kx}$, or equivalently if ${\frac{y}{x}=k}$ for a constant ${k}$.
2. A proportional relationship must go through the origin so determining if a relationship is proportional can be done very quickly with a graph.
3. To increase speed, find the ratio of output to input in two cases. In a proportional relationship these will be identical.

## Real-life Applications

1. Businesses can use proportions to figure out how much money they will earn if they sell more products.